Statistical Mechanics of Turbulent Flows / Edition 1

by Stefan Heinz

Overview

The simulation of technological and environmental flows is very important for many industrial developments. A major challenge related to their modeling is to involve the characteristic turbulence that appears in most of these flows. The traditional way to tackle this question is to use deterministic equations where the effects of turbulence are directly parametrized, i. e. , assumed as functions of the variables considered. However, this approach often becomes problematic, in particular if reacting flows have to be simulated. In many cases, it turns out that appropriate approximations for the closure of deterministic equations are simply unavailable. The alternative to the traditional way of modeling turbulence is to construct shastic models which explain the random nature of turbulence. The application of such models is very attractive: one can overcome the closure problems that are inherent to deterministic methods on the basis of relatively simple and physically consistent models. Thus, from a general point of view, the use of shastic methods for turbulence simulations seems to be the optimal way to solve most of the problems related to industrial flow simulations. However, it turns out that this is not as simple as it looks at first glance. The first question concerns the numerical solution of shastic equations for flows of environmental and technological interest. To calculate industrial flows, 3 one often has to consider a number of grid cells that is of the order of 100 .

Product Details

ISBN-13:	9783642072611
Publisher:	Springer Berlin Heidelberg
Publication date:	12/07/2010
Edition description:	Softcover reprint of hardcover 1st ed. 2003
Pages:	216
Product dimensions:	8.27(w) x 10.98(h) x 0.24(d)

Table of Contents

Introduction: The basic equations; Turbulence models; Filter operations.- Shastic variables: PDFs of one variable; The characterization of PDFs by moments; PDFs of several variables; Statistically most-likely PDFs; Examples for statistically most-likely PDFs; Examples for other PDFs; Theta and delta functions.- Shastic processes: PDF transport equations; The Fokker-Planck equation; An exact solution to the Fokker-Planck equation; Shastic equations for realizations; Shastic modeling; The dynamics of relevant variables.- The equations of fluid and thermodynamics: The fluid dynamic variables; From the molecular to fluid dynamics; The closure of the fluid dynamic equations; The equations for multicomponent reacting systems; Direct numerical simulation; Reynolds-averaged Navier-Stokes equations; Second- and higher-order RANS equations.- Shastic models for large-scale turbulence: A hierarchy of shastic velocity models; The generalized Langevin model for velocities; A hierarchy of Langevin models; The Kolmogorov constant; A hierarchy of shastic models for scalars; Compressible reacting flow: velocity models; Compressible reacting flow: scalar models; Shastic models and basic equations; Consistent turbulence models; Nonlinear shastic models.- Shastic models for small-scale turbulence: The generalization of LES by FDF methods; The closure of the equation for filtered velocities; The closure of the scalar FDF transport equation; The closure of LES and FDF equations; The dynamic eddy length scale calculation; The scalar-conditioned convective flux; An assumed-shape FDF method.- The unification of turbulence models: The need for the unification of turbulence models; Unified turbulence models; Some unsolved questions. References.- Author index.- Subject index.

Editorial Reviews

To summarise, this is a monograph on the method of stochastic modelling of turbulent fluid flow, comprising the necessary prerequisites and the main features of the method, up to the present research level. It deserves attention by the specialists and the beginners as well and has useful applications. It is clearly presented, with careful argumentation and interesting scientific contents. The book's use is nicely supported by an extended list of all symbols and abbreviations and, of course, with references. The reviewer can well recommend it.
—European Journal of Mechanics B/Fluids 23, 795-796

S. Grossmann

This book offers a timely survey of techniques in modern computational fluid mechanics for turbulent flows with reacting scalars. It should be of interest to engineers, while the discussion of the underlying tools, namely pdfs, stochastic and statistical equations should also be attractive to applied mathematicians and physicists. The book's emphasis on local pdfs and stochastic Langevin models gives a consistent structure to the book and allows the author to cover almost the whole spectrum of practical modelling in turbulent CFD. ... In short, the book is orientated more towards applications than towards turbulence theory; it is written clearly and concisely and should be useful to a large community, interested either in the underlying stochastic formalism or in CFD applications.
—J. Phys. A: Math. Gen. 37, 9603-9604.

C. Cambon

The book, within the constraints of size does provide a valuable survey of stochastic turbulent flow procedures supplementary to and in comparison with more conventional closure procedures. Considering the book's relatively modest price it would be a useful addition for personal as well as institutional acquisition.
—Appl. Mech. Rev. 57, B28-B29

A. C. Buckingham

From the reviews:

"This book is a descriptive monograph with a focus on shastic probability density function (pdf) procedures and their implementation for turbulent flow. … The book includes a usefully extensive reference list, author and subject index. … The book … does provide a valuable survey of shastic turbulent flow procedures supplementary to and in comparison with more conventional closure procedures. Considering the book’s relatively modest price it would be a useful addition for personal as well as institutional acquisition." (AC Buckingham, Applied Mechanics Reviews, Vol. 57 (5), 2004)

"This is a nicely written textbook, aiming to present the methods of shastic modelling of turbulent fluid flow. … The author nicely and convincingly expands on the advantages of shastic modelling … . It deserves attention by the specialists and the beginners as well and has useful applications. It is clearly presented, with careful argumentation and interesting scientific contents. The book’s use is nicely supported by an extended list of all symbols and abbreviations and, of course, with references. The reviewer can well recommend it." (Dr. S.Grossmann, European Journal of Mechanics B/Fluids, Issue 23, 2004)

"This is a handbook for a computational approach to reacting flows … . This book offers a timely survey of techniques in modern computational fluid mechanics for turbulent flows with reacting scalars. It should be of interest to engineers, while the discussion of … pdfs, shastic and statistical equations should also be attractive to applied mathematicians and physicists. … it is written clearly and concisely and should be useful to a large community, interested either in the underlying shastic formalism or in CFD applications." (C Cambon, Journal of Physics A: Mathematical and General, Vol. 37 (40), 2004)

From the Publisher